↑

Properties

Label 2015.2.ee
Level $2015$
Weight $2$
Character orbit 2015.ee
Rep. character $\chi_{2015}(131,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $1024$
Sturm bound $448$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 2015 = 5 \cdot 13 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2015.ee (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 31 \)
Character field: \(\Q(\zeta_{15})\)
Sturm bound: \(448\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2015, [\chi])\).

Total New Old
Modular forms 1824 1024 800
Cusp forms 1760 1024 736
Eisenstein series 64 0 64

Trace form

\( 1024 q - 264 q^{4} + 4 q^{6} + 128 q^{9} + O(q^{10}) \) \( 1024 q - 264 q^{4} + 4 q^{6} + 128 q^{9} + 4 q^{10} - 4 q^{13} + 24 q^{14} + 16 q^{15} - 240 q^{16} + 12 q^{17} + 48 q^{19} + 12 q^{21} + 4 q^{22} - 24 q^{23} - 80 q^{24} - 512 q^{25} + 36 q^{27} - 32 q^{29} - 52 q^{31} - 12 q^{33} - 28 q^{34} - 24 q^{35} - 496 q^{36} + 40 q^{37} + 52 q^{38} - 104 q^{40} + 20 q^{41} + 264 q^{42} + 8 q^{43} + 132 q^{44} + 72 q^{46} + 44 q^{48} + 104 q^{49} + 80 q^{51} - 12 q^{52} + 36 q^{53} - 272 q^{54} - 16 q^{56} + 80 q^{57} - 104 q^{58} - 68 q^{59} - 12 q^{60} + 72 q^{61} - 24 q^{62} + 16 q^{63} - 232 q^{64} - 8 q^{65} + 64 q^{66} - 32 q^{67} - 124 q^{68} + 32 q^{69} + 40 q^{71} - 396 q^{72} - 48 q^{73} + 64 q^{74} + 72 q^{76} - 152 q^{77} + 8 q^{79} + 8 q^{81} + 88 q^{82} + 32 q^{83} + 464 q^{84} - 4 q^{85} + 44 q^{86} - 8 q^{87} + 60 q^{88} + 48 q^{89} + 64 q^{90} - 60 q^{93} - 144 q^{94} - 8 q^{96} + 32 q^{97} - 24 q^{98} - 80 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2015, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(2015, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2015, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(31, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(155, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(403, [\chi])\)\(^{\oplus 2}\)